@article{Tian2023, 
author = {Wenyan Tian and Yaoyao Chen and Zhaoxia Meng and Hongen Jia},
title = {An adaptive finite element method based on Superconvergent Cluster Recovery for the Cahn-Hilliard equation},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {3},
pages = {1323-1343},
keywords = {error estimate, the Cahn-Hilliard equation, adaptive, SCR},
url = {https://www.sciopen.com/article/10.3934/era.2023068},
doi = {10.3934/era.2023068},
abstract = {In this study, we construct an error estimate for a fully discrete finite element scheme that satisfies the criteria of unconditional energy stability, as suggested in [1]. Our theoretical findings, in more detail, demonstrate that this system has second-order accuracy in both space and time. Additionally, we offer a powerful space and time adaptable approach for solving the Cahn-Hilliard problem numerically based on the posterior error estimation. The major goal of this technique is to successfully lower the calculated cost by controlling the mesh size using a Superconvergent Cluster Recovery (SCR) approach in accordance with the error estimation. To demonstrate the effectiveness and stability of the suggested SCR-based algorithm, numerical results are provided.}
}